Force field (physics)
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In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, a force field is a vector field corresponding with a
non-contact force A non-contact force is a force which acts on an object without coming physically in contact with it. The most familiar non-contact force is gravity, which confers weight. In contrast a contact force is a force which acts on an object coming physic ...
acting on a particle at various positions in
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
. Specifically, a force field is a vector field \vec, where \vec(\vec) is the force that a particle would feel if it were at the point \vec.


Examples

*
Gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
is the force of attraction between two objects. A gravitational force field models this influence that a massive body (or more generally, any quantity of
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
) extends into the space around itself. In
Newtonian gravity Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distan ...
, a particle of mass ''M'' creates a
gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
\vec=\frac\hat, where the radial unit vector \hat points away from the particle. The gravitational force experienced by a particle of light mass ''m'', close to the surface of
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
is given by \vec = m \vec, where ''g'' is the
standard gravity The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. ...
. *An
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
\vec is a vector field. It exerts a force on a
point charge A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take u ...
''q'' given by \vec = q\vec.Calculus: Early Transcendental Functions, by Larson, Hostetler, Edwards, p1055
/ref>


Work

Work is dependent on the displacement as well as the force acting on an object. As a particle moves through a force field along a path ''C'', the
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal t ...
done by the force is a
line integral In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''curvilinear integral'' are also used; ''contour integral'' is used as well, alt ...
: W = \int_C \vec \cdot d\vec This value is independent of the
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
/momentum that the particle travels along the path.


Conservative force field

For a conservative force field, it is also independent of the path itself, depending only on the starting and ending points. Therefore, the work for an object travelling in a closed path is zero, since its starting and ending points are the same: : \oint_C \vec \cdot d\vec = 0 If the field is conservative, the work done can be more easily evaluated by realizing that a conservative vector field can be written as the gradient of some scalar potential function: : \vec = -\nabla \phi The work done is then simply the difference in the value of this potential in the starting and end points of the path. If these points are given by ''x'' = ''a'' and ''x'' = ''b'', respectively: : W = \phi(b) - \phi(a)


See also

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Field line A field line is a graphical visual aid for visualizing vector fields. It consists of an imaginary directed line which is tangent to the field vector at each point along its length. A diagram showing a representative set of neighboring field ...
*
Force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
*
Force field (technology) In speculative fiction, a force field, sometimes known as an energy shield, force shield, energy bubble or deflector shield, is a barrier made of things like energy, negative energy, dark energy, electromagnetic fields, gravitational fields, ...
*
Psychokinesis Psychokinesis (from grc, ψυχή, , soul and grc, κίνησις, , movement, label=ㅤ), or telekinesis (from grc, τηλε, , far off and grc, κίνησις, , movement, label=ㅤ), is a hypothetical psychic ability allowing a person ...
*
Stasis field A stasis or stasis field, in science fiction, is a confined area of space in which time has been stopped or the contents have been rendered motionless. Overview A stasis field is imagined to be a region in which a stasis process is in effect. S ...
*
The Force The Force is a metaphysical and ubiquitous power in the '' Star Wars'' fictional universe. "Force-sensitive" characters use the Force throughout the franchise. Heroes like the Jedi seek to "become one with the Force", matching their personal wi ...
*
Tractor beam A tractor-beam is a device with the ability to attract one object to another from a distance. The concept originates in fiction: The term was coined by E. E. Smith (an update of his earlier "attractor-beam") in his novel ''Spacehounds of IPC'' (19 ...


References


External links


Conservative and non-conservative force-fields
University of Texas at Austin Force {{Electromagnetism-stub